Statistical Tests

Abstract

IN discussions on statistical tests with various Continental statisticians and users of statistical methods, I have been struck by their universal mistrust of modern statistical tests as developed by Pearson, Fisher and other workers in Great Britain. I have come to the conclusion that the main reason for this attitude is a perfectly sound reason, namely, that a test is used by many workers in Great Britain as a simultaneous test of the untruth of one hypothesis and the truth of the reverse hypothesis. There is in fact a large region in the distribution of the criterion for which neither a hypothesis nor its reverse can be assumed to be true. One or the other is true, of course, but the test cannot help us in coming to a decision on the matter. Judgment must be reserved. For example, we may wish to test whether a given sample differs significantly from a random sample from a normal population. Applying the ² test, after finding the best fitting normal distribution, and using p = 0.05, say, as the level of significance, we may find that our sample is just not significantly abnormal.